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I wanted to see what I could do in a hurry using the commands found at Forecasting: Principles and Practice . I chose a simple enough data set of Wisconsin Unemployment from 1976 to the present (April 2013). I kept the last 12 months worth of data to test the accuracy of the models. The next blog post will include a multiple regression analysis. The analysis is lacking many important steps, particularly the ARIMA, but this is a down and dirty exercise.

library(forecast)
library(lmtest)
library(caret)
#http://www.quandl.com/FRED-Federal-Reserve-Economic-Data/WIUR-Unemployment-Rate-in-Wisconsin

#Using Quandl data, great little site

#some minor clean up
colnames(wi)<-c('date', 'rate')
wi$date<-as.Date(wi$date)
summary(wi)

#base data, 1-436, test data 437-448

wi.b<-wi[1:436,]
wi.p<-wi[437:448,]
wi.ts<-ts(wi.b$rate, start=c(1976, 1), frequency=12) wi.p.ts<-ts(wi.p$rate, start=c(2012, 5), frequency=12)
plot.ts(wi.ts)

#Lets test some models
mean<-meanf(wi.ts, 12)
naive<-rwf(wi.ts, 12)
s.naive<-snaive(wi.ts, 12)
drift<-rwf(wi.ts, 12, drift=T)

#linear fit
m1<-tslm(wi.ts~trend)
m2<-tslm(wi.ts~trend+season)

#checking for autocorrelation
res1 <- residuals(m1)
par(mfrow=c(1,2))
plot(res1, ylab="Residuals",xlab="Year")
Acf(res1, main="ACF of residuals")

res2 <- residuals(m2)
par(mfrow=c(1,2))
plot(res2, ylab="Residuals",xlab="Year")
Acf(res2, main="ACF of residuals")
par(mfrow=c(1,1))

#Durbin-Watson Test
dwtest(m1, alt="two.sided")
dwtest(m2, alt="two.sided")
#yep autocorrelation city! No surprize here, due to the nature of unemployment

#STL ETS Decomposition
m3<-stl(wi.ts, s.window='periodic')
plot(m3)
m4<-ets(wi.ts, model='ZZZ')
plot(m4)

#ARIMA
m5<-auto.arima(wi.ts)
plot(forecast(m5, h=12))
#neural networks
m6<-nnetar(wi.ts)
m6
plot(forecast(m6, h=12))

#Testing for accuracy the first 4 models
a1<-accuracy(mean, wi.p.ts)
a2<-accuracy(naive, wi.p.ts)
a3<-accuracy(s.naive, wi.p.ts)
a4<-accuracy(drift, wi.p.ts)

a.table<-rbind(a1, a2, a3, a4)

#Creating the forecast and accuracy for the next 6 models
f1<-forecast(m1, h=12)
f2<-forecast(m2, h=12)
f3<-forecast(m3, h=12)
f4<-forecast(m4, h=12)
f5<-forecast(m5, h=12)
f6<-forecast(m6, h=12)

a5<-accuracy(f1, wi.p.ts)
a6<-accuracy(f2, wi.p.ts)
a7<-accuracy(f3, wi.p.ts)
a8<-accuracy(f4, wi.p.ts)
a9<-accuracy(f5, wi.p.ts)
a10<-accuracy(f6, wi.p.ts)

#Combining into a table with row names
a.table<-rbind(a.table, a5, a6, a7, a8, a9, a10)
row.names(a.table)<-c('Mean', 'Naive', 'S. Naive', 'Drift', 'Lm~Trend',
'Lm~Trend+Sea', 'STL', 'ETS', 'ARIMA', 'Neuro')

#make into a data frame so the best model is first, according to MAPE
a.table<-as.data.frame(a.table)
a.table<-a.table[order(a.table\$MAPE),]
a.table

Results so far: Looks like the mean like forecasts are doing the best, the fancy models are not doing very well.